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This is the Prime Pages' interface to our BibTeX database.  Rather than being an exhaustive database, it just lists the references we cite on these pages.  Please let me know of any errors you notice.
References: [ Home | Author index | Key index | Search ]

Item(s) in original BibTeX format

@unpublished{Shevelev2008,
  AUTHOR =       {V. Shevelev},
  TITLE =        {Overpseudoprimes, {M}ersenne numbers and {W}ieferich primes},
  NOTE =         {avaliable from \url{http://arxiv.org/abs/0806.3412}},
  year =         {2008},
  month =        {July},
  abstract =     {We introduce a new class of pseudoprimes-so called "overpseudoprimes" which is a special
  subclass of super-Poulet pseudoprimes. Denoting via $h(n)$ the multiplicative order of 2 modulo $n,$ we
  show that odd number $n$ is overpseudoprime iff value of $h(n)$ is invariant of all divisors $d>1$ of $n.$
  In particular, we prove that all composite Mersenne numbers $2^p-1,$ where $p$ is prime, and squares of
  Wieferich primes are overpseudoprimes. We give also a generalization of the results on arbitrary base $a>1$
  and prove that every overpseudoprime is strong pseudoprime of the same base.}
}

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